We present a pair of coupled equations that shows the nonlinear coupling between a newly discovered low-frequency dispersive electromagnetic mode and flute-like electrostatic convective cells in a non-uniform dusty magnetoplasma. From the coupled mode equations we obtain a nonlinear dispersion relation, which predicts efficient excitation of convective cells at the expense of the dispersive electromagnetic wave energy. The relevance of our investigation to the transfer of energy from short-scale electromagnetic waves to long-scale convective cells in tokamak plasmas is pointed out.

The paper is concerned with the influence of magnetic field shear on the structure of Alfvén waves standing along field lines in the one-dimensionally inhomogeneous box model of the magnetosphere, enclosed between two parallel, infinitely conducting planes (ionospheres). We consider the transverse small-scale Alfvén waves whose azimuthal component of the wave vector $k_y$ satisfies the condition $k_y l\,{\gg}\,1$, where $l$ is the distance between the ionospheres. For this model, the Alfvén resonance condition has been established. It is shown that resonance can also occur at a constant Alfvén velocity if the field-line inclination to the ionosphere is changed. On resonant magnetic shells there occurs a singularity of the wave field of the same kind as in the absence of shear. Moreover, there are found many resemblances between Alfvén-wave behavior in our one-dimensionally inhomogeneous model and in two-dimensional inhomogeneous models with plasma and magnetic field parallel inhomogeneity taken into account. Thus, the presence of shear leads to a difference of the frequencies of poloidal and toroidal oscillations of field lines, and to the dependence of the wave's frequency on the transversal components of wave vector. Then, in the sheared magnetic field with highly conductive boundaries the source excites multiple standing Alfvén harmonics at different locations. In general, the localization regions of different longitudinal harmonics overlap. However, in the small but finite shear limit, a total wave field represents a set of mutually isolated transparent regions corresponding to different harmonic numbers. In each of these regions the waves are found to be travelling across the magnetic shells, and the transparent region is limited in the coordinate $x$ by two turning points, at one of which the mode is poloidally polarized, and the other point it is toroidally polarized (it is at this latter point where Alfvén resonance occurs). Furthermore, the phase velocity of the wave is directed toward the poloidal point, and the group velocity is directed at the toroidal point.

The basic equations for a layer of an electrically conducting fluid are considered in the magnetohydrodynamic approximation. An electric field is applied parallel to the layer. Because of various instabilities, turbulent fluid motions will be generated in general. The goal of the analysis presented in this paper is the derivation of upper bounds for the average turbulent resistivity of the layer. In order to demonstrate the concept of the upper bound theory, only the simplest case will be treated and the boundary conditions will be assumed in such a way that the analogy with the problem of bounds on the momentum transport in a turbulent Couette layer can be utilized.

An expansion is developed of the two-point correlation function in the two-time correlation functions up to the expansion terms of third order. This expansion is necessary for the rigorous derivation of kinetic equations that objectively describe physical phenomena in a ‘single’ plasma with Langmuir turbulence. The correspondence of the expansion terms with various physical processes of the traditional weak plasma turbulence theory is discussed. Perspectives are outlined of application of the results to studies in the physics of non-ideal plasmas.

Previous computations concerning the allowed magnetohydrodynamic steady states of a visco-resistive magnetofluid in a toroid are extended. The current is supported by an externally imposed toroidal electric field, and a scalar resistivity and viscosity are assumed. Emphasis is on the character of the necessary velocity fields (mass flows) that toroidal geometry demands. Non-ideal boundary conditions are imposed at the toroidal boundary. One of the more interesting results to emerge is the sensitive dependence of the flow pattern on the shape of the toroidal cross-section boundary: the dipolar poloidal flow that had appeared for cross sections that were symmetric about the midplane is seen to deform continuously into a monopolar pattern for a ‘D-shaped’ cross section as the viscous Lundquist number $M$ is increased. A net toroidal mass flow also develops. A boundary layer whose properties scale with fractional powers of $M$ is also studied. The interior of the magnetofluid is approximately force-free, with current densities and magnetic fields that are nearly parallel for JET-like parameters. Steep velocity derivatives and a steep pressure drop in this boundary layer become steeper with increasing $M$ (decreasing viscosity). The magnetic quantities do not reflect the rapid velocity and vorticity variations in the boundary layer. The maximum velocities, in the region where the viscosity is large enough for the numerics to work, are of the order of a few hundreds of centimetres per second. Measurements of velocity fields confined to the boundary layer would misrepresent the interior plasma conditions. Uncertainties in the magnetized plasma viscosity remain as an obstacle to unambiguous tests of the results in the case of real plasmas.

The propagating source method has been extended to solve the Boltzmann equation with a quasi-linear diffusion scattering operator. A half-range polynomial expansion method is used to reduce the integral-diffusion form of the ‘collisional’ Boltzmann equation to an infinite set of linear hyperbolic partial differential equations in the harmonics of the polynomial expansion. The lowest-order truncation of the coupled set of equations yields an inhomogeneous form of the well-known telegrapher equation, which, unlike the homogeneous telegrapher equation, does not introduce physically unrealistic pulse solutions. Anisotropic quasi-linear scattering models for which the index $q$ of the power spectrum of magnetic fluctuations satisfies $1\,{<}\,q\,{<}\,2$ admit slow scattering through $90^{\circ}$ and no scattering through $90^{\circ}$ for $q \,{\ge}\,2$. Accordingly, four models that either allow or enhance scattering through $90^{\circ}$ are used to augment the standard quasi-linear model for pitch-angle scattering. These are mirroring, dynamical turbulence and two distinct wave-based models. In the case that mirroring is responsible for scattering particles through $90^{\circ}$, together with the standard QLT (quasi-linear theory) pitch-angle diffusion model for scattering within the forward and backward hemispheres, it is found that the QLT isotropic and anisotropic models are well approximated by relaxation time scattering models. As an application of the general study, the implications of the four models introduced to redress the difficulties faced by QLT in describing scattering through $90^{\circ}$ are briefly considered. An initial beam was found to relax more rapidly for either the dynamical turbulence or wave models with resonant scattering through $90^{\circ}$ than for mirroring models.

In recent years, ablative plasma generated by capillary discharge attracted considerable attention because of its possible applications in electrothermal launchers, laser-driven particle accelerators, thin-film deposition and soft X-ray lasers, etc. An electrical discharge through a capillary insulator heats the capillary plasma that provides further evaporation of the capillary wall and electrode. The created plasma is confined by the capillary wall, electrode material and flow in a specified chamber through a hollow electrode. The mass flux leaving the capillary in axial motion is replenished by a radial inward flow of matter. Thus the radial component of the mass flux plays a principal role in the mass and energy balance. In this paper, we present a theoretical model for a time-dependent magneto-hydrodynamical simulation to calculate the dynamic evolution of plasma flow and transportation in two-dimensional configurations combined with turbulent effect. The thermodynamic and transport properties are characterized by a model that describes the plasma composition, equation of state, internal energy, viscosity and thermal and electrical conductivity for a partially ionized multi-component plasma in the weakly non-ideal region, similar to that which exists in the ablation-controlled arcs. Our model results show that some of the well-known experimental features of this kind of discharge are confirmed, particularly the radial mass and energy transportation.

We develop a fully nonlinear theory of electrostatic stationary waves of the ion-cyclotron-acoustic type propagating in a magnetized plasma. The analysis is facilitated by the existence of two fundamental constants of the motion, namely conservation of momentum flux parallel to the ambient field, and conservation of energy in the direction of propagation of the wave. These lead to the structure of the waves being governed by a first-order differential equation for the longitudinal ion flow speed and, therefore, its properties are readily analysed. In the case of subsonic wave speeds, compressive soliton wave structures propagate in a cone of obliquity around the magnetic field. If the wave speed is supersonic, the waves are oscillatory in nature, and asymmetric about the compressive and rarefactive phases, essentially because, in the compressive phase, the flow is driven towards its sonic point, whereas in the rarefactive phase, the flow is driven away from its sonic point. As the initial ‘driver’ field approaches a critical value, the end point of the compression coincides with the sonic point, with the result that the waveform in the flow speed (and potential) forms a cusp. It is possible that this feature may provide an explanation for the spiky waveforms observed by FAST and other similar satellite observations.

The parametric instability of parallel-propagating circularly polarized Alfvén waves (pump waves) is revisited. The stability of these waves is determined by the linearized system of magnetohydrodynamic equations with periodic coefficients. The variable substitution that reduces this system of equations to a system with constant coefficients is suggested. The system with constant coefficients is used to derive the dispersion equation that was previously derived by many authors with the use of different approaches. The dependences of general stability properties on the dimensionless amplitude of the pump wave $a$ and the ratio of the sound and Alfvén speed $b$ are studied analytically. It is shown that, for any $a$ and $b$, there are such quantities $k_1$ and $k_2$ that a perturbation with the dimensionless wavenumber $k$ is unstable if $k_1^2<k^2<k_2^2$, and stable otherwise. It is proved that, for any fixed $b$, $k_2$ is a monotonically growing function of $a$. The dependence of $k_1$ on $a$ is different for different values of $b$. When $b^2<1/3$, $k_1$ is a monotonically decreasing function of $a$. When $1/3<b^2<1$, $k_1$ monotonically decreases when $a$ varies from zero to $a_c(b)$, takes its minimum value at $a = a_c$ and then monotonically increases when $a$ increases from $a_c$ to infinity. When $b > 1$, $k_1$ is a monotonically increasing function of $a$. For any $b$, $k_1$ tends to a limiting value approximately equal to 1.18 as $a \to \infty$.

An analytical and numerical study of the ideal magnetohydrodynamic (MHD) spectrum of waves and instabilities of a cylindrical plasma column with flows is presented. Our analytical results are relevant for thermally stratified, rotating, magnetized cylindrical equilibria. The presence of azimuthal flow makes the general analysis of the MHD spectrum difficult, except in cases where the continuous parts of the spectrum are absent. In the presence of Doppler shifted Alfvén and slow continua, a local analysis at resonant surfaces or internal extrema can provide a simple and reliable way to access information on MHD spectroscopy. In this paper, local cluster conditions, which govern the occurrence of sequences of discrete global modes, have been generalized for rotating equilibria. The generalized Suydam criterion for instability is revisited. A numerical study confirms our analytical results and clearly demonstrates how the local criteria govern the existence of the accumulating eigenmodes.

Alfvén waves are considered in a radial flow and external magnetic field, which relates to some features of the solar wind near the critical point. The Alfvén wave equation for the velocity perturbation is derived, showing that it has in general two singularities (besides the origin and infinity), namely a critical layer (at real distance), where the Alfvén speed equals the mean flow velocity, and a transition level (at imaginary distance), where the spatial derivative of the flow velocity equals the wave frequency. It is shown that in the case of mean flow velocity varying as a power of radial distance the wave field is specified at all distances by a combination of solutions of the Alfvén wave equation around three singularities: a regular singularity at the center, so that ascending power-series solutions exist, some with logarithmic terms; an irregular singularity at infinity, leading to the non-existence of any solution as an ascending Frobenius–Fuchs series, and the existence of two solutions as ascending–descending Laurent series; the region of validity of the preceding solutions is limited by a regular singularity at a finite, non-zero radial distance, which is the critical layer, where the flow velocity and Alfvén speed are equal. The wave field is singular at the critical layer, and has an amplitude jump, which is illustrated by plotting the wave field in the neighborhood of the critical layer, for several values of dimensionless frequency and Alfvén number, combined into a single parameter. When considering Alfvén waves in the solar wind, at least three kinds of boundary conditions could be applied: (i) an initial condition specifying the wave field at the surface of the Sun; (ii) an asymptotic condition excluding wave sources at infinity, by specifying an outward-propagating wave (radiation condition); (iii) a finiteness condition that the wave field be finite at the critical layer. Since the Alfvén wave equation is of second order, only two conditions can in general be applied. It is shown, for example, that (ii) and (iii) are generally incompatible. If the conditions (i) and (iii) are chosen, i.e. an initial wave field is given and the radiation condition of outward propagation at infinity is met, then (ii) will not in general be met; thus the wave field would be singular at the critical layer, in the absence of dissipation, corresponding to the resonance of a linear undamped system. It is shown that in the presence of dissipation, either by fluid viscosity or Ohmic resistivity, the wave field would be finite at the critical layer, corresponding to the resonance of a linear damped system.

An analysis of electron trajectories in a helical magnetic wiggler with a uniform ion channel and a uniform axial magnetic field is presented. The axial field is considered in both the conventional and reversed directions. Equations for the transverse coordinates and velocities of a single relativistic electron in the combined ion electrostatic field and helical and axial magnetic fields are derived. A sixth-degree polynomial equation for the electron velocity and an equation for the function $\Phi$ (which determines the rate of change of axial velocity with energy) are derived. Results of some numerical calculations are presented to illustrate the effects of the electrostatic field and the axial magnetic field in each of the two configurations.

In the present investigation, the growth of a radially symmetric ripple, superimposed on a single intense laser beam in a collisionless unmagnetized plasma, taking into account the relativistic nonlinearity, is presented. The effect of the position and the width of the ripple on its growth have been studied in some detail. In addition to the growth of the ripple, the effect of the presence of the ripple on the excitation of plasma wave has also been studied.

In the context of ion-acoustic waves in a magnetized plasma comprising cold ions and non-isothermal electrons, the present authors have previously shown small amplitude, weakly nonlinear waves to be governed by a modified version of the Zakharov–Kuznetsov equation. In this paper, we consider a plane solitary travelling-wave solution to this equation that propagates at an angle $\alpha$ to the magnetic field, where $0\,{\le}\,\alpha\,{\le}\,\pi$. The multiple-scale perturbation method developed by Allen and Rowlands is used to calculate the growth rate of a small, transverse, long-wavelength perturbation. To first order there is instability for $0\,{\le}\,\sin\alpha\,{<}\,\sin\alpha_{\rm c}$, where the critical angle $\alpha_{\rm c}$ is identified. At second order, the singularity which apparently occurs in the growth rate at $\alpha\,{=}\,\alpha_{\rm c}$ is removed by using a method devised by Allen and Rowlands; then it is found that there is also instability for $\sin\alpha\,{\ge}\,\sin\alpha_{\rm c}$. A numerical determination for the growth rate is given for the instability range $0\,{<}\,k\,{<}\,3$, where $k$ is the wavenumber of the perturbation. For $k|{\rm sec}\,\alpha|\,{\ll}\,1$, there is excellent agreement between the analytical and numerical results. The results in this paper agree qualitatively with those of Allen and Rowlands for the Zakharov–Kuznetsov equation.

Collisionless electron heating in a low-pressure weakly magnetized inductively coupled plasma is considered by means of quasilinear theory. We use a one-dimensional slab model of an inductively coupled plasma with a penetrating radio frequency (RF) electric field given by an exponential function. Diffusion coefficients in velocity space are obtained regarding the induced RF electric field and induced polarization electric field (DC electric field). It is shown that the induced polarization electric field has a significant contribution to the collisionless electron heating. We consider the influence of the quasilinear collision integral on the evolution of the symmetric part of the electron energy distribution function.

The linear stability of tearing modes in a cylindrical plasma subject to a sub-Alfvénic equilibrium shear flow along the equilibrium magnetic field is considered. The equations in the resistive boundary layer at the rational surface are solved numerically using a Fourier transform combined with a finite-element approach. The behaviour of the growth rate as a function of the flow and the various parameters (including a perpendicular fluid viscosity) is obtained. Marginal stability curves showing the dependence of the familiar matching parameter $\Delta'$ with flow and shear are also given.

The transport of neutral hydrogen atoms in a hydrogen plasma is investigated. An analytical approach based on a polynomial expansion technique is used to solve boundary value problems for half-space and slab plasma. A linear version of the Boltzmann equation is considered to describe the transport of the neutrals. Particular and complete solutions are obtained for specular and diffuse reflections. The numerical results are reported.

This paper presents the possible periodic solutions and the solitons of the cubic–quintic nonlinear Schrödinger equation. Corresponding to five types of different structures of the pseudo-potentials, five types of periodic solutions are given explicitly. Five types of solitons are also obtained explicitly from the limiting procedures of the periodic solutions. This will benefit the study of the generation of fast ions or electrons, which are produced from the soliton breaking when the plasma is irradiated a high-intensity laser pulse.

In this paper, we add a supplementary contribution and support to the path integral method by exploring the theory of radiation in plasma physics. This method, based on the Feynman path integral formalism, has the advantage of treating the electrons and ions on the same physical basis and both time-independent and time-dependent problems on the same footing. Since the main quantity in the problem of plasma radiation is the dipolar autocorrelation function of the radiator, we derive it using the path integral technique in its perturbative form. We show that the dipolar autocorrelation function could be written as a generalized expression taking into account the time-dependency effects.

The effect of an external magnetic field on an ion–dust two-stream instability in a collisional dusty plasma is investigated. We consider the parameter regime in which the ions and electrons are strongly magnetized, while the charged dust is unmagnetized. The presence of a magnetic field tends to hinder the growth of the instability. The implications for laboratory dusty plasmas such as ‘plasma crystals’ are discussed.